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We present analytic models for the blocking probability of both unique path and multiple path multistage interconnection networks under the assumption of either permutation or random memory request patterns. The blocking probability of an interconnection network under the assumption of permutation requests is a quantitative measure of the network's permutation capability. We compare the performance of networks with approximately equivalent hardware complexity. It is shown that variations of banyan networks can be designed with extremely low blocking probabilities under the assumption of permutation requests.